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View Full Version : odds to come on turn and river? how 2 calculate?

Schizo
01-10-2005, 02:41 AM
I know how to calculate for river, but what about turn and river combo?

gaming_mouse
01-10-2005, 05:58 AM
[ QUOTE ]
I know how to calculate for river, but what about turn and river combo?

[/ QUOTE ]

What is your question? You need to give an example or something.

Lost Wages
01-10-2005, 10:56 AM
With "X" number of outs and two cards to come there are three possibilities:

1) You catch 2 outs
2) You catch 1 out
3) You catch 0 outs

Sometimes you don't mind catching 2 outs and sometimes you would rather not. For example, if you have 7/images/graemlins/spade.gif6/images/graemlins/spade.gif and the board is A/images/graemlins/heart.gif7/images/graemlins/club.gif2/images/graemlins/diamond.gif, you have 5 outs to trips or two pair. If you catch a 7 or 6 on the turn you really don't mind another on the river. However, if you have 7/images/graemlins/spade.gif6/images/graemlins/spade.gif and the board is J/images/graemlins/spade.gifT/images/graemlins/spade.gif2/images/graemlins/heart.gif giving you 9 outs to a flush, you would really prefer not to catch 2 outs.

For #1 you need to hit the turn and river so the probability is just:
(X/47)*((X-1)/46)

For #2, P(one out)= P(out on turn*blank on river) + P(blank on turn*out on river):
(X/47)*((46-X-1)/46) + ((47-X)/47)*(X/46)

For #3, you simply need to miss twice:
((47-X)/47)*((46-X)/46)

Usually you just ask, "What is the probability of hitting at least one out by the river?", ignoring the small chance of hitting 2 outs. In that case, you simply add #1 and #2 above. Or more simply, you take the probability of catching zero outs (#3) and subtract that from 1.

To convert probability to odds:
If the probability is P, the the odds are ((1-P)/P):1

Of course, all of that is much too difficult to use at the table so a chart is in order:
<font class="small">Code:</font><hr /><pre> Odds:1
F to T T to R F to R
Outs (1 or 2)
1 46.0 45.0 22.5
2 22.5 22.0 10.8
3 14.7 14.3 7.0
4 10.8 10.5 5.1
5 8.4 8.2 3.9
6 6.8 6.7 3.1
7 5.7 5.6 2.6
8 4.9 4.8 2.2
9 4.2 4.1 1.9
10 3.7 3.6 1.6
11 3.3 3.2 1.4
12 2.9 2.8 1.2
13 2.6 2.5 1.1
14 2.4 2.3 1.0
15 2.1 2.1 0.9
</pre><hr />

Lost Wages

gamble4pro
01-10-2005, 03:53 PM
I assume you want to know how calculate the odds for events of "hit at turn or river" type.
The best way of calculating card odds, in order to avoid the errors, is to use combinations.
In your request, the events whose probability you are looking for are occurences of certain 2-card combinations on the board (turn + river).
Basically, you have 5 seen cards (if you frefer to odds for own hand, i.e 2 hole cards and the flop cards.
You have to count the favorable 2-card combinations (turn + river for your expected formation) and divide this number by C(47,2) = 1081.
Or, you may consider the independent events:
hit by turn and not hit by river
hit by turn and hit by river
not hit by turn and hit by river
not hit by turn and not hit by river